I have a 2004 Mazda 6 with 145000 miles. The car has a noticible stumble every now and then, especially going uphill. Any suggestions?

 

Many things more than likely need replacing with that mileage. I am not going to get in to a war about it. If it happens uphill (with a load on the car) try downshifting 1 gear to give it more rpm when going up every hill.

 

UseyourNoggin is correct.
Most likely you need a tune up. Plugs, wires, air filter, basic stuff.

 

Happening more frequently, or under heavy acceleration, could indicate a vacuum leak. The accordion air inlet tube is notorious for developing cracks.